PRMIA 8008 Online Practice Questions and Exam Preparation

PRMIA 8008 Online Questions & Answers

• Question 31:

  Which of the following contributed to the systemic failure during the credit crisis that began in 2007?

  A. Stress tests that did not stress enough
  B. Moral hazard from the strategy of 'originate and distribute'
  C. Inadequate attention paid to liquidity risk
  D. All of the above
  D. All of the above

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  Explanation

  All the factors listed above contributed to systemic failure. Liquidity risk was not on the radar of regulators, and was a second priority for risk managers, and most of the focus was on capital adequacy as liquidity was thought to be an unlikely problem. Liquidity, regardless of capital adequacy, was the primary cause of failure of a number of institutions during the crisis.

  Similarly, stress tests proved to be much milder than the shocks that were actually experienced, and the strategy of 'originate and distribute' implied that the mortgage and other debt originators had no interest in any due diligence as they intended to package and sell the debt to other investors.

  Therefore Choice 'd' is the correct answer.

• Question 32:

  The generalized Pareto distribution, when used in the context of operational risk, is used to model:

  A. Tail events
  B. Average losses
  C. Unexpected losses
  D. Expected losses
  A. Tail events

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  Explanation

  Some risk experts have suggested the use of extreme value theory to model tail risk or extreme events for operational risk. The generalized Pareto model or the Peaks-over- Threshold (POT) model are often used to model extreme value distributions, and therefore Choice 'a' is the correct answer.

• Question 33:

  If A and B be two debt securities, which of the following is true?

  A. The probability of simultaneous default of A and B is greatest when their default correlation is +1
  B. The probability of simultaneous default of A and B is not dependent upon their default correlations, but on their marginal probabilities of default
  C. The probability of simultaneous default of A and B is greatest when their default correlation is negative
  D. The probability of simultaneous default of A and B is greatest when their default correlation is 0
  A. The probability of simultaneous default of A and B is greatest when their default correlation is +1

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  Explanation

  If the marginal probability of default of two securities A and B is P(A) and P(B), then the probability of both of them defaulting together is affected by the default correlation between them. Marginal probability of default means the probability of

  default of each security on a standalone basis, ie, the probability of default of one security without considering the other security.

  The relationship that expresses the probability of joint default of the two is given by the following expression:

  

  It is easy to see that in a situation where the Default Correlation of A and B = 0, ie, the defaults are independent, the combined probability of default is P(A)*P(B), exactly what we would intuitively expect. Also in the other extreme case where the default correlation is equal to 1 and P(A) = P(B) = p, ie the securities behave in an identical way, the expression resolves to just p, which is what we would expect. From the above relationship, it is clear that the probability of joint default of A and B is the greatest when default correlation between the two is equal to 1, ie the securities behave in an identical way. Therefore Choice 'a' is the correct answer.

• Question 34:

  Which of the following losses can be attributed to credit risk:

  I - Losses in a bond's value from a credit downgrade II - Losses in a bond's value from an increase in bond yields III - Losses arising from a bond issuer's default IV - Losses from an increase in corporate bond spreads

  A. I, III and IV
  B. II and IV
  C. I and II
  D. I and III
  D. I and III

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  Explanation

  Losses due to credit risk include the loss of value from credit migration and default events (which can be considered a migration to the 'default' category). Therefore Choice 'd' is the correct answer. Changes in spreads or interest rates are examples of market risk events. [Discussion: It may be argued that losses from spreads changing could be categorized as credit risk and not market risk. The distinction between credit and market risk is never really watertight. The reason I have called it market risk in this question is because spreads can change due to two reasons: first, due to the individual issuer going down in their credit rating (whether issued or perceived, as we have witnessed in Europe sovereign debt), and second due to the spread for the overall category changing due to macro fundamentals with nothing changing for the individual issuer. For example the spread between municipal bonds and treasuries may be small during boom times and may expand during recessions - regardless of how the individual issuer has been doing. Clearly, the first case is credit risk and the second is probably market risk. A change in overall corporate bond spreads is something I would consider akin to a rate change - which is why I have called it as not a part of credit risk. But an alternative perspective may not be incorrect either.]

• Question 35:

  The standalone economic capital estimates for the three business units of a bank are $100, $200 and $150 respectively. What is the combined economic capital for the bank, assuming the risks of the three business units are perfectly correlated?

  A. 450
  B. 269
  C. 21
  D. 72500
  A. 450

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  Explanation

  Since the business units are perfectly correlated, we can get the combined EC as equal to the sum of the individual EC estimates. Therefore Choice 'a' is the correct answer.

• Question 36:

  For a given mean, which distribution would you prefer for frequency modeling where operational risk events are considered dependent, or in other words are seen as clustering together (as opposed to being independent)?

  A. Binomial
  B. Gamma
  C. Negative binomial
  D. Poisson
  C. Negative binomial

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  Explanation

  An interesting property that distinguishes the three most used distributions for modeling event frequency is that for a given mean, their variances differ. The ratio of variance to mean (the variance-mean ratio, calculated as variance/mean) can then be used to decide the kind of distribution to use. Both the variance and the mean can be estimated from available data points from the internal or external loss databases, or the scenario exercise. The variance-mean ratio reflects how dispersed a distribution is. (In the PRMIA handbook, the variance to mean ratio has been described as the "Q-Factor".) The Poisson distribution has its mean equal to its variance, and therefore the variance to mean ratio is 1. For the negative binomial distribution, this ratio is always greater than 1, which means there is greater dispersion compared to the mean - or more intervals with low counts as well as more intervals with high counts. For the binomial distribution, the variance to mean ratio is less than one, which means it is less dispersed than the Poisson distribution with values closer to the mean. In a situation where operational risk events are seen as clustering together, or dependent, the variance will be higher and it would be more appropriate to use the negative binomial distribution.

• Question 37:

  For a given notional amount, which of the following carries the greatest counterparty exposure (assuming the same counterparty credit rating for each):

  A. A futures contract on an equity index
  B. A one year certificate of deposit
  C. A one year forward foreign exchange contract
  D. A one year interest rate swap
  B. A one year certificate of deposit

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  Explanation

  The exposure at default is the greatest for the certificate of deposit as the entire notional amount is exposed to the risk of default. The other choices represent derivatives for which the current replacement value, which would be far less than

  notional, would be the credit exposure.

  Said another way - if the counterparty were to default, the entire money in the CD would be at risk, whereas for the derivative contracts it would only be the replacement value that would be at risk.

• Question 38:

  Which of the following formulae correctly describes Component VaR. (p refers to the portfolio, and i is the i-th constituent of the portfolio. MVaR means Marginal VaR, and other symbols have their usual meanings.)

  

  A. III
  B. II
  C. I
  D. I and II
  D. I and II

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  Explanation

  The first two formulae describe component VaR. The last formula is the formula for Marginal VaR. Therefore I and II is the correct answer. Component VaR is a VaR decomposition technique that allows the total VaR for a portfolio to be broken down and attributed to the components of a portfolio. The total of the component VaR for each constituent of a portfolio is equal to the VaR for the portfolio. This property is extremely useful as opposed to the standalone VaR for each constituent taken alone as it can be used for allocating trading budgets.

• Question 39:

  Fill in the blank in the following sentence:

  Principal component analysis (PCA) is a statistical tool to decompose a ____________ matrix into its principal components and is useful in risk management to reduce dimensions.

  A. Covariance
  B. Correlation
  C. Volatility
  D. Positive semi-definite
  D. Positive semi-definite

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  Explanation

  PCA is a statistical tool that decomposes a positive semi-definite matrix into its principal components. The first few principal components explain nearly all the variation and other components can then be ignored as they are too small in the larger picture. PCA in risk management is applied to a positive semi-definite correlation or covariance matrix to reveal the principal components that cause the variation. By allowing a focus on a few components, PCA reduces dimensionality.

  While performing the math of PCA is unlikely to be asked in the PRMIA exam, you should remember that principal components have the additional property of being uncorrelated to each other which makes it useful as it is possible to vary one of the components without having to worry about the effect of that on the other components.

• Question 40:

  What is the annualized steady state volatility under a GARCH model where alpha is 0.1, beta is 0.8 and omega is 0.00025?

  A. 0.0025
  B. 0.08
  C. 0.1
  D. 0.05
  D. 0.05

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  Explanation

  Steady state variance under the GARCH model is given by the formula /(1 - ?). In this case, steady state variance therefore works out to 0.00025/(1 - 0.1 - 0.8) = 0.0025. Since this is the variance, volatility is the square root of 0.0025, which works out to 0.05. Thus, 5% (=0.05) is the correct answer, and the others are incorrect.

  Also recall the following in respect of GARCH: